In our model, each node \(i \in \lbrace 1\ldots N\rbrace \)  of the network has a state (or spin) \(s_i\)  and a (constant) threshold \(T_i\) . The classical Ising model translates to the a majority rule (MR) model, where all thresholds are exactly \(0.5\) : a spin tends to flip to the state where it will be aligned with more than one half its neighboring spins, see Ch. 8 [1]}. This system is Hamiltonian with the energy function: \(\mathcal {H} = -\frac{1}{2}\sum \nolimits _{i;j\in \langle i\rangle } s_is_j\) , where \(i \in 1\ldots N\) , and \(\langle i\rangle \)  refers to the network neighbors of node \(i\) .
